What problem does Russell’s paradox reveal about unrestricted set formation?

Russell’s paradox reveals that an unrestricted comprehension principle in set theory leads to logical inconsistency. This principle previously allowed for the formation of a set based on any definable condition, including the set of all sets that do not contain themselves: $R=\{x|x\notin x\}$.1

The paradox arises because $R$ is a member of itself if and only if it is not a member of itself, creating a vicious circle that renders the system contradictory.1

This discovery demonstrated that one cannot simultaneously assume the existence of a universal totality of all sets while permitting unfettered set construction. To resolve this, modern systems like Zermelo-Fraenkel (ZF) set theory impose restrictions on comprehension, ensuring that no set can be as large as the universe of all sets, thereby precluding the existence of a universal set.1